Question: Simplify the following expression: $ q = \dfrac{n - 9}{-9} - \dfrac{-1}{6} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{n - 9}{-9} \times \dfrac{6}{6} = \dfrac{6n - 54}{-54} $ Multiply the second expression by $\dfrac{-9}{-9}$ $ \dfrac{-1}{6} \times \dfrac{-9}{-9} = \dfrac{9}{-54} $ Therefore $ q = \dfrac{6n - 54}{-54} - \dfrac{9}{-54} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{6n - 54 - 9 }{-54} $ Distribute the negative sign: $q = \dfrac{6n - 54 - 9}{-54}$ $q = \dfrac{6n - 63}{-54}$ Simplify the expression by dividing the numerator and denominator by -3: $q = \dfrac{-2n + 21}{18}$